Lectures on the Fourier Transform and Its Applications

This book provides a comprehensive introduction to Fourier analysis for engineering and science students, covering topics such as distributions, the generalized Fourier transform, and higher-dimensional phenomena. It aims to cultivate advanced mathematical know-how and increase confidence in learning and using mathematics.

\n Format: Hardback
\n Length: 702 pages
\n Publication date: 01 March 2019
\n Publisher: American Mathematical Society
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This book is a comprehensive resource for engineering and science students seeking to develop advanced mathematical knowledge and proficiency in Fourier analysis. Written as a lecture notes for a course at the advanced undergraduate or beginning graduate level, it goes beyond teaching specific topics and techniques and aims to cultivate a deeper understanding of mathematics and enhance students' confidence in learning and applying it.

The author's primary goal is to help engineering and science students broaden their mathematical horizons and develop a strong foundation in advanced mathematical concepts. By emphasizing the coherence of the subject and presenting mathematics in a relatable and engaging manner, the book aims to inspire students to appreciate the beauty and power of mathematics.

The section headings in the book are familiar to mathematicians, but the arrangement and emphasis are tailored to students from other disciplines. The material provides a solid foundation for advanced courses in signal processing and imaging, and it is suitable for both undergraduate and graduate students.

With over 200 problems, many of which are oriented toward applications, the book offers a wealth of practical exercises to reinforce the concepts learned. Additionally, the use of standard software in many of the problems makes it accessible to students without extensive technical backgrounds.

One unique feature of this book is its detailed and accessible treatment of distributions and the generalized Fourier transform. These topics are often overlooked in courses aimed at engineers, but they are essential for understanding many modern applications in fields such as signal processing, image analysis, and physics. The book provides a clear and comprehensive introduction to these topics, making them accessible to students with a basic understanding of calculus and linear algebra.

Furthermore, the book offers more coverage of higher-dimensional phenomena than is typically found in books at this level. This includes discussions of vector spaces, matrices, and tensors, which are fundamental tools in many areas of mathematics and engineering. By presenting these topics in a clear and concise manner, the book helps students build a strong foundation in multidimensional analysis and apply it to real-world problems.

In conclusion, this book is a valuable resource for engineering and science students who want to develop advanced mathematical knowledge and proficiency in Fourier analysis. With its comprehensive coverage of topics, practical exercises, and accessible writing style, it provides a solid foundation for students seeking to pursue careers in fields such as signal processing, imaging, and mathematics. Whether you are a beginner or an experienced student, this book will help you deepen your understanding of mathematics and unlock its potential for solving complex problems.

\n Weight: 1340g\n
Dimension: 192 x 265 x 37 (mm)\n
ISBN-13: 9781470441913\n \n